This invention relates to an art that extracts effective features for the pattern recognition, and thereby carries out stably the pattern recognition.
The pattern recognition art that determines a category of the unknown pattern is needed in various fields. As one of the pattern recognition art, Watanabe et al (S. Watanabe, N. Pakvasa, Subspace method of pattern recognition, Proc. 1st Int. J. Conf. on Pattern Recognition, 1973) propose the subspace method. The subspace method is advantageous in that feature extraction and classification can be executed at the same time and extension is easy from two categories to a plurality of categories. In the subspace method, a similarity is determined by angle between an input vector converted from an unknown pattern and a reference subspace. The reference subspace is generated by the principal component analysis from a previously obtained vector of one category. When the similarity is equal to or greater than a threshold, the input vector can be determined the category.
JP-A-11(1999)-265452 and Maeda et al (K. Maeda, T. Watanabe, A Pattern Matching Method with Local Structure, IEICE Trans. D-II Vol. J68-D, No. 3, 345-352, 1985) propose the mutual subspace method which determines similarity by angle between the input subspace and the reference subspace. The mutual subspace method is more robust against pattern variations and noise because of using an input subspace instead of an input vector. The similarity S between subspace P and subspace Q is calculated by the following equation.S=cos2 θ  (1)where θ represents the angle between P and Q. This angle is called canonical angle.
If two subspaces are equal, then θ=0. Described in JP-A-11(1999)-265452 cited before, cos2 θ is obtained by determining a maximum eigenvalue of the following matrix X.
                    Xa        =                  λ          ⁢                                          ⁢          a                                    (        2        )                                          X          =                      (                          x              ij                        )                          ,                  (                      i            ,                          j              =                              1                ~                N                                              )                                    (        3        )                                          (                      x            ij                    )                =                              ∑                          1              ≤              k              ≤              N                                ⁢                                    (                                                ψ                  i                                ,                                  ϕ                  k                                            )                        ⁢                          (                                                ϕ                  k                                ,                                  ψ                  j                                            )                                                          (        4        )            where ψi represents an i-th basic vector on the subspace P. φj represents an j-th basic vector on the subspace Q. N represents the number of dimensions of the subspace.
Furthermore, in order to enhance the recognition accuracy for the mutual subspace method, JP-A-2000-30065 and Fukui et al (K. Fukui, O. Yamaguchi, K. Suzuki, K. Maeda, Face Recognition under Variable Lighting Condition with Constrained Mutual Subspace Method—Learning of Constraint Subspace to Reduce Influence of Lighting Changes—, IEICE Trans. D-II Vol. J82-D-II, No. 4, 613-620, 1999) propose the constrained mutual subspace method. This technique is that the input subspace and the reference subspace are projected onto a constraint subspace for emphasizing extra-category variation which is considered effective for the pattern recognition. The similarity Sc under the constrained mutual subspace method, determined by an angle θc between subspace Pc and subspace Qc which are projected onto a constraint subspace C (Equation (5)).SC=cos2 θC   (5)
The procedure of projection onto a constraint subspace is detailed in JP-A-2000-30065 and Maeda et al cited on p.2. The procedure of generating a constraint subspace is described in the JP-A-2000-30065.
When the constraint subspace is used for the pattern recognition, recognition performance becomes unstable because the similarity of a certain category becomes low. If the constraint subspace is changed, the similarity of another category becomes low. For example on the face image recognition system, the person who is occurred with such problem is prone to higher false rejection rate than other persons.